Question

1. A sum of three numbers is 315. If the ratio between 1st
and 2ndis 2:3 and the ratio between 2nd and 3rd is 4:5,Find
the 2nd number.​

Answer 1

${ \underbrace{ \textsf{ \textbf{Given : }}}}$

$\rm \odot \: The \: sum \: of \: three \: numbers \: is \: 315$

$\rm \odot \: Ratio \: of \: {1}^{st} and \: {2}^{nd} no. \: is \: 2 : 3$

$\rm \odot \: And \: ratio \: between \: {2}^{nd} \: and \: {3}^{rd} no. \: is \: 4: 5$

${ \underbrace{ \textsf{ \textbf{To \: find : }}}}$

✴️ The numbers.

${ \underbrace{ \textsf{ \textbf{Solution : }}}}$

The ratio of 1st and 2nd no. :

➠ Ratio of 1st and 2nd number :- 2 : 3

➠ Ratio of 1st and 2nd number :- 2 × 4 : 3 × 4

➠ Ratio of 1st and 2nd number :- 8 : 12

The ratio of 2nd and 3rd number :-

➠ Ratio of 2nd and 3rd number :- 4 : 5

➠ Ratio of 2nd and 3rd number :- 4 × 3 : 5 × 3

➠ Ratio of 2nd and 3rd number :- 12 : 15

The ratio of the numbers we are getting now :

1st : 2nd : 3rd - 8 : 12 : 15

Let's assume :

✴️ The numbers are : $\rm 8x, \: 12x, \: 15x, \:$

$〄\begin{gathered}\underline{\boldsymbol{According\: to \:the\: question :}}\\\end{gathered}$

$\rm : \implies 8x + 12x + 15x = 315$

$\rm : \implies \: 35x = 315$

$\rm : \implies \: x = { \cancel{\frac{315}{35}}}$

$\rm : \implies \: x = 9$

After solving we get :

x = 9

Hence

✴ The numbers are :

$\rm \: 8x = 8 \times 9 = 72 ☑$

$\rm \: 12x = 12 \times 9 = 108 ☑$

$\rm \: 15x = 15 \times 9 = 135 ☑$

Answer 2

${ \underbrace{ \textsf{ \textbf{Given : }}}}$

$\begin{gathered}\rm •\: The \: sum \: of \: three \: numbers \: is \: 315 \\\end{gathered}$

$\begin{gathered}\rm •\: Ratio \: of \: {1}^{st} and \: {2}^{nd} no. \: is \: 2 : 3 \\\end{gathered}$

$\begin{gathered}\rm •\: And \: ratio \: between \: {2}^{nd} \: and \: {3}^{rd} no. \: is \: 4: 5 \\ \end{gathered}$

${ \underbrace{ \textsf{ \textbf{To \: find : }}}}$

☃️The numbers.☃️

${ \underbrace{ \textsf{ \textbf{Solution : }}}}$

The ratio of 1st and 2nd no. :

➠ Ratio of 1st and 2nd number :- 2 : 3

➠ Ratio of 1st and 2nd number :- 2 × 4 : 3 × 4

➠ Ratio of 1st and 2nd number :- 8 : 12

The ratio of 2nd and 3rd number :-

➠ Ratio of 2nd and 3rd number :- 4 : 5

➠ Ratio of 2nd and 3rd number :- 4 × 3 : 5 × 3

➠ Ratio of 2nd and 3rd number :- 12 : 15

The ratio of the numbers we are getting now :

1st : 2nd : 3rd - 8 : 12 : 15

Let's assume :

✴️ The numbers are : 8x, 12x, 15x,8x,12x,15x

$\begin{gathered} \begin{gathered}\underline{\boldsymbol{According\: to \:the\: question :}}\\\end{gathered}\end{gathered}$

$\begin{gathered}\rm : \implies 8x + 12x + 15x = 315 \\ \end{gathered}$

$\begin{gathered}\rm : \implies \: 35x = 315 \\\end{gathered}$

$\begin{gathered}\rm : \implies \: x = { \cancel{\frac{315}{35}}} \\\end{gathered}$

$\begin{gathered}\rm : \implies \: x = 9 \\ \end{gathered}$

After solving we get :

x = 9

Hence

✴ The numbers are :

$\begin{gathered}\rm \: 8x = 8 \times 9 = 72 ☑ \\\end{gathered}$

$\begin{gathered}\rm \: 12x = 12 \times 9 = 108 ☑\\\end{gathered}$

$\begin{gathered}\rm \: 15x = 15 \times 9 = 135 ☑ \\ \end{gathered}$

HOPE THIS HELPS ☺️❤️

BE BRAINLY ⚡☃️